Wavelet shrinkage estimators of Hilbert transform

被引：1

作者：

Chen, Di-Rong ^{[1
]}

Zhao, Yao ^{[1
]}

机构：

[1] Beijing Univ Aeronaut & Astronaut, Dept Math, LMIB, Beijing 100083, Peoples R China

来源：

JOURNAL OF APPROXIMATION THEORY | 2011年 / 163卷 / 05期

关键词：

Wavelets shrinkage; Hilbert transform; Nonstandard form; Maximal operator; COMPACTLY SUPPORTED WAVELETS; CONVERGENCE; OPERATORS; EXPANSIONS; BASES;

D O I：

10.1016/j.jat.2011.02.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given signal and is widely used in data compression, signal processing, statistics, etc. Based on wavelet shrinkage estimators of the original function f, we construct the estimators of its Hilbert transform H f with the help of a representation due to Beylkin, Coifman and Rokhlin. The almost everywhere convergence and norm convergence of the proposed estimators are established. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：652 / 662

页数：11

共 50 条

[21] Parkinson’s disease detection from speech using combination of empirical wavelet transform and Hilbert transform
Sachin Anap
Satish Jondhale
Balasaheb Agarkar
Sachin Chaudhari
International Journal of Speech Technology, 2025, 28 (1) : 185 - 194
[22] The Hilbert transform of cubic splines
Abd-el-Malek, Mina B.
Hanna, Samer S.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 80 (80):
[23] Rellich identities for the Hilbert transform
Carro, Maria J.
Naibo, Virginia
Soria-Carro, Maria
JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (04)
[24] ON THE MAXIMAL DIRECTIONAL HILBERT TRANSFORM
Laba, I.
Marinelli, A.
Pramanik, M.
ANALYSIS MATHEMATICA, 2019, 45 (03) : 535 - 568
[25] The Algorithm of Testing ADC Effective Number of Bits Based on Hilbert and Wavelet Transform
Awada, Emad A.
PROCEEDINGS OF 3RD INTERNATIONAL CONFERENCE ON INFORMATION SYSTEM AND DATA MINING (ICISDM 2019), 2019, : 196 - 200
[26] On the study of applying Morlet wavelet to the Hilbert transform for the envelope detection of bearing vibrations
Sheen, Yuh-Tay
MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2009, 23 (05) : 1518 - 1527
[27] Hilbert transform pairs of orthonormal symmetric wavelet bases using allpass filters
Zhang, Xi
Ge, Dong Fang
2007 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-7, 2007, : 425 - 428
[28] A novel scheme for the design of approximate Hilbert transform pairs of orthonormal wavelet bases
Shi, Hongli
Hu, Bo
Zhang, Jian Qiu
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2008, 56 (06) : 2289 - 2297
[29] A new combined method for RMS calculation based on wavelet packet and Hilbert transform
Modarresi, Javad
Hooshmand, Rahmat-Allah
TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES, 2016, 24 (04) : 3178 - +
[30] On computing with the Hilbert spline transform
Micchelli, Charles A.
Xu, Yuesheng
Yu, Bo
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2013, 38 (03) : 623 - 646

← 1 2 3 4 5 →